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From: Ludovicus on 5 Aug 2010 19:05
As the other statistical distributions, the gaps between primes
deserves its own distribution.
It is very irregular and I have not found the appropriate distribution
to be applied.
Marek.Wolf developed a formula for the probability P(N) of a gap d,
in the neighborhood of a large N.:

P(N) = C.EXP[-d / Ln(N)] / (Ln N)^2

C varies with the divisibility of gap. The larger corresponds to the
multiples of 6. In that case C= 3.
I propose the name of "Wolf distribution" for that type of
distribution.
See "Unexpected regularities in the distribution of prime numbers"
Marek Wolf
http://www.ift.uni.wroc.pl/~mwolf

For the frequency of primes in equal intervals the Binomial
Distribution was proposed by Emil Borel (1935) and adjusts very well.
Also the Gumbel Distribution for the frequency of divers extreme
values, behaves well.
The discrete Exponential Distribution have many applications in
primes.
Ludovicus
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